{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 使用PCA去噪"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 回忆我们之前的例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.empty((100, 2))\n",
    "X[:,0] = np.random.uniform(0., 100., size=100)\n",
    "X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0, 5, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dJG1KuUji+qVABu2nHva89160PtWj5G755qOcMXoa42Oj6m4ohaaALonrlwIZNOcd9rzv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e59cf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "X_reduction = pca.transform(X)\n",
    "X_restore = pca.inverse_transform(X_reduction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+w8tvTLFh1dh55RUv27dB5JKL9aTa8kqj3iuvnZ7i3nXLncDNcEK3HrS1eIj7v/XKO93e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\nhG5mlhNO6GZmOeGEbmaWE/8fZyVKVOb/HicAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1119a04a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_restore[:,0], X_restore[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "降维的过程可以理解成是去噪。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 手写识别的例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "digits = datasets.load_digits()\n",
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noisy_digits = X + np.random.normal(0, 4, size=X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "example_digits = noisy_digits[y==0,:][:10]\n",
    "for num in range(1,10):\n",
    "    example_digits = np.vstack([example_digits, noisy_digits[y==num,:][:10]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Pz6dzsA9wWFhYiRwf651lZrZ27VqYf/DBB0Uev7jY8ZmZValSxUaPHu3JN27c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\n7t27w31Vr17dauxr166p70lwcLC6vta8NNfIkSPVHH1OCKrAEhGJjIy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06tTJan30/RAR\nGTt2rCPTqsJyBQcHq1VVqOKpefPmcF8VK1ZU8/fff1/NUV8rE9QzsnPnzmp+5513wgoxDepNKIKr\nw1BV3Lp169QcVTaLiDRp0sTw6uyg6jBThTF6f1EVoW0Vn4jII4884shCQkLyvT1/ESIiIiLX4kSI\niIiIXIsTISIiInItToSIiIjItTgRIiIiItf67xp0/L/jx49bbzNw4EA1nz17tponJSWpeaVKleAY\n48ePt3pNHo9H7XszatQodX1TjyVkyZIl1tsgM2fOLJT91K9fX81Lly4Nt0GfOaru03qc3YipBxHi\n6+srxYsXd+SogtDUB+jFF19U86FDh6r56tWrb/wC80B9vUzraxWXmZmZ6vqmvmioWhB9tqhv2Usv\nvQTHQD3eCkuJEiXgsjFjxqj5/Pnz1XzNmjVq3rdvXziGTWXKjZw7d856m/vuu0/N0TWrRYsWam6q\nmDty5Igjy8jIyMer+yt0ndmzZw/cpl69emo+ceJENY+Li1PzCxcuwDEKcp2xYapsrl27tprv379f\nzVF12N69e+EY99xzj+HV6S5duiQ//PCDI2/cuLG6/oEDB+C+0PcNnQ9abzsRc/Xtf4u/CBEREZFr\ncSJERERErsWJEBEREbkWJ0JERETkWpwIERERkWtxIkRERESuZVU+n5mZKSdOnHDkWrnyjaAyTkQr\n5RO53gAPQc0jp0yZArfRSilRU0lTU9caNWqoOWqmh5iaCNo2lUxOTpbPP//ckbdr105df9q0aXBf\n6PPbuXOnmhcrViwfr/Cvnn76aettENTkt3///nCbbdu2qfmcOXOsxt63bx9cZir/1ly5ckW2b9/u\nyIsU0b/KqImxCC7dv3LlipqjMlit4WFBJSYmqk0q0eeESnBFzMeuQY8/2LFjB9zm/PnzVmOIXG9S\nrTW8RY/j+Pjjj+G+XnvtNaux0es1NXbVHolhKp+/cOGC+pgQ1LDTdD1u2bKlmqNmzagJ7+nTp+EY\n6JEfSHp6uloujppzm95b9BgZlC9atEjNTY1rCyIgIMDq0Rdvv/02XNa+fXs1T0xMVPOClMn/+OOP\njsymITJ/ESIiIiLX4kSIiIiIXIsTISIiInItToSIiIjItTgRIiIiItfyeL3e/K/s8SSLCL4F/uZR\nwev1RuYNeXw3DfX4RG79Y+Tx3TRu9XP0Vj8+EZ6jN/sxwuPLy2oiRERERHQr4X+NERERkWtxIkRE\nRESuxYkQERERuZZVi42IiAhvTEyMI0f3GRWktUC5cuXUPCsrS81Nj9EuWbKkmv/6668p2k1UYWFh\n3tKlSzvWDwwMVPdz8eJFOHZSUpKa33777Vb7CgsLg2Ogx+UfPXpUPT70+Z06dUrdT3p6Ohwbve8R\nERFqHh4ebj0GWnby5En1+P5/fG+FChUcOXq9AQEBcPzDhw+rOTqWqKgouC8kJydHzXft2mX1GaLj\n++OPP+DYQUFBal65cmW4jebatWtwma+vr5qj7yA6vuzsbHU/Z8+ehWNr7YBE8GeOWgWha5IJOj4R\nkdDQUK/W1iEtLU3dl+n9RW05UPsU1E4CnQtIfHy8pKSkeLRl6DPMzMxU93XmzBk4DrqOonMU/S1C\nbZJMbM9RxHSNO3r0qJpHR0erOWp/o/3dypWcnKzmJ06cMF5HtWNE5+i5c+fg+KiVRpUqVdQ8JCRE\nzU1tXbQWQwkJCXL27Fn1HHVsn5+VcsXExKh9d9AkBR2oiEjbtm3VfOzYsWqO3sw1a9bAMTp16qTm\nHo9HvRu+dOnSMnv2bEdes2ZNdT8rV66EY0+cOFHNFyxYoOaop1iHDh3gGGhf7du3V48PfX6oT8zB\ngwfh2OvWrVPz2NhYNUefhWkMrZ+PiMigQYNgNUOFChVk8+bNjnz9+vXq+nfddRccv3HjxmretWtX\nNe/Xrx/cF4ImMMWLF7f6DNeuXavuB/WRExGpV6+emq9atQpuo7lw4QJchv7Bg76D6PjQH3zUc0oE\nfx4VK1ZU8yZNmqj5+PHj4RgIOj6R65MR7fqwf/9+dX3TP7i03oEiuP/bq6++quamnm2aOnXqwGXo\nM0xISFDXHzduHNwXeu/R9RVNGgvSi8v2HEXQdUwEXxeHDBmi5lqfQRGRwYMHwzFQz81+/frBcxQd\nI/pxY+7cuXD8ESNGqLntuYsmjSL6jx6PPfYYXD8v/tcYERERuRYnQkRERORanAgRERGRa3EiRERE\nRK5ldbM04ufnp+bx8fFwm08++UTNjx8/ruboJrhFixaZX5yFS5cuyerVqx05uln6xRdfhPvyePSb\n1VE1B7qZF92ILoJvKrP1zjvvqHm1atXgNvfff7+aoxvjWrVqpeb33nsvHKN169ZqPmjQILjNqVOn\n5N1333XkI0eOVNc3VQSh6oX+/fureUFulkZVIEhSUpJMmDDBkffo0UNd/5VXXoH7Qp/V8uXL1Rx9\nhqh6UQTfLG0LFV6gSi8RfHMuukHfVN2DHDp0yHobj8ejVrmgm9ebNm0K9zVv3jw1RzdYo3O0fPny\ncAztOnfp0iW4fmpqqmzcuNGR33333er606ZNg/tq3769mo8ZM0bN0fnQrFkzOIbpxm8bH3/8sZq/\n/vrrcJtnnnlGzZ9++mmrsUeNGgWX9e3bV81N16ucnBy1Qgz9Hba5eTwX+vu5bNkyNa9evbrV/lHF\nqoa/CBEREZFrcSJERERErsWJEBEREbkWJ0JERETkWpwIERERkWtZVY1lZmaq/XtQdZjpseYNGzZU\nc1TtYOpbhph69Gj8/PyMPVvy6t69O1yGKiHKli2r5rt371Zz1A5AxL4H0tWrV9W7+1HVBOq1JXL9\nEew2UIXCP//5T7gNanlgUqZMGVghpomLi4PL7rnnHquxUXUPqnAREfHxsfu3yG233aa2Sdi2bZu6\nPqoMExEZMGCAmqPH+6OqMVOLjQ0bNsBlaF9Lly515DVq1FDXR33yRK6f75otW7aouem7hpjaCCHo\nOrNw4UK4PvLDDz+oOWpBgV7v4sWL4Rha+wJTtV5wcLA8/PDDjnzr1q3q+qY+YPPnz4fLNMOGDVNz\nVMUrIrJp0yY1Rz0m09PT1cpD1L7E9HfozTffVHNUQYjew8KGKv/Q+dOtWze4L1R1jSqlUSWmqR2T\nbZVdXvxFiIiIiFyLEyEiIiJyLU6EiIiIyLU4ESIiIiLX4kSIiIiIXIsTISIiInItq/L5okWLquXf\nkZGR6vpHjhyB+1q5cqWaP/7442req1evfLzCv7JpuiYiEh4eLi+88IIj3759u7o+aggoImpTRRH7\nxnwtW7aEY9jy9fVVS1VRqf93330H94XKVBFUio+ahYqIfP/991ZjiFwvVdWagKISWVSmKiLyxhtv\nqDlqcIhe75IlS+AY2uMoCqJu3bpqbmoMjBofozJg9AgLU3m3qZmnpkSJEmqzXdSAt1KlSnBf6Jox\nc+ZMNUdNQTt16gTHKIiMjAz5448/HHnv3r3V9dG1RERk4MCBVmOjBpzoGl4QKSkp8sUXXzjyDh06\nqOujUn8RkTZt2liNPWXKFDXXyvlzmcr3NQEBAVK1alVHvnnzZnX9Pn36wH01atRIzVFTW9Ro2/Qe\nVqhQAS5DfH19JSwszJGjx6ZcvnwZ7uvYsWNqjh4FgBrRmq6jJ0+edGSmhuV58RchIiIici1OhIiI\niMi1OBEiIiIi1+JEiIiIiFyLEyEiIiJyLauqsRMnTshbb73lyFFVhalpZ/Xq1a1ydCe5qRFbQRoi\nasLDw63Hfvnll9UcVVuhppJdu3aFY6CmdYi/v79UrlzZkWvZjaCGqKjRZe3atQttDBNU7XD06FF1\nfdRIVARXSJw+fdpqX8WKFYNjFOS918ybN0/N77vvPrjNuXPn1Dw4OFjN+/fvr+YrVqyAYxRWVRyC\nPlcRXOUWHR2t5qh5rGkMU9UaEhoaKk8++WS+10fNcUVwQ9+UlBQ1//nnn9X8yy+/hGOYKg81xYsX\nVxsQh4SEqOujBtwiIl6v12rsyZMnq7mpOW9OTo7VGDk5OWqVFGrSfObMGbgv1JBUa44tItKzZ081\nRxWHBeXr66s21kXVbKYG1ajhLWo4u2zZMjUvVaoUHEP7rqelpcH18+IvQkRERORanAgRERGRa3Ei\nRERERK7FiRARERG5FidCRERE5FpWVWMlS5aUjh07OnLUo8d0xz/q/dSgQQM1R2NoPV9yHTp0CC7T\nZGZmqlUuqDIE9VAREbntttvUHFUDoH5fiYmJcIzCgnpnmXrFodcbGBio5lq1oYhItWrV4Bimijnk\n/PnzsmDBAkf+2muvqeujfjciIk899ZSao2qkv+OzQlAfp+XLl8NtTL17NF26dFHz3bt3w21Q9SSS\nnJwsn3/+uSO//fbb1fVNFTmoWuXPP/9Uc1QdNXfuXDjGoEGD4LK/A7rGbtu2Tc0XLlyo5uPGjYNj\npKen53tckes9KcuVKweX56VVed7IgQMH1Bz1l9u/fz/cl6kqUOPj4wMr4DR79uyBy7Kzs9W8Tp06\nav7oo4+qOXo/ROyri0VwPzV0jUPViCK4DyLq4enjo/8+Y6ou1M5RreoN4S9CRERE5FqcCBEREZFr\ncSJERERErsWJEBEREbkWJ0JERETkWlZVY2lpabJ3715HHhQUpK5v6vWFqsPq16+v5qi6B/V9EhGJ\nioqCyzRFixaVsmXL5nv9devWwWWof01cXJyaoyqMCRMmwDFs+hWJXP/8tAqG2NhYdf3jx4/DfY0e\nPVrNUQXatWvX1Fzr2ZML9S0z8ff3t+r/ZOozhD4r1HuuT58+ao6ql0Ts+uGIXD9PtEqTIkX0rzLq\n3SeC+xYNHz5czYcMGaLmpn5p33zzjZqj73OJEiWkdevWjhz1GTK9t5988omao/f8hx+lt7J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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11420e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(10, 10, figsize=(10, 10),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "    gridspec_kw=dict(hspace=0.1, wspace=0.1)) \n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "plot_digits(example_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.5).fit(noisy_digits)\n",
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cnlVbmfEmmKw67O9//zvMXQ0J2XnABEEAK5VYc1NWbWlmVqdOHZiz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\nsKDzGEXnIfuR+fbbb+n43bp1gzn70XjvvfdgftZZZ9ExChc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IiEiwNBESERGRYGkiJCIi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\nSxMhERERCZYmQiIiIhKs/wf8/lVGUtZj9QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114045278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(example_digits)\n",
    "filtered_digits = pca.inverse_transform(components)\n",
    "plot_digits(filtered_digits)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
